The 21-year-old was stretchered off during Saturday's 2-0 win over Motherwell in the Scottish Premiership.
Matthews was subsequently forced to pull out of the Welsh squad for their upcoming World Cup qualifiers against Macedonia and Belgium.
An official Celtic statement read: "Adam Matthews saw a specialist today (Monday), and he will undergo shoulder surgery on Wednesday. It's likely that he will be out for between 10-12 weeks."
Matthews joined the club from Cardiff City in the summer of 2011.